Dissertations / Theses: 'Free vibration of plate'

1

Chattopadhyay, Arka Prabha. "Free and Forced Vibration of Linearly Elastic and St. Venant-Kirchhoff Plates using the Third Order Shear and Normal Deformable Theory." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/102661.

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Employing the Finite Element Method (FEM), we numerically study three problems involving free and forced vibrations of linearly and nonlinearly elastic plates with a third order shear and normal deformable theory (TSNDT) and the three dimensional (3D) elasticity theory. We used the commercial software ABAQUS for analyzing 3D deformations, and an in-house developed and verified software for solving the plate theory equations. In the first problem, we consider trapezoidal load-time pulses with linearly increasing and affinely decreasing loads of total durations equal to integer multiples of the time period of the first bending mode of vibration of a plate. For arbitrary spatial distributions of loads applied to monolithic and laminated orthotropic plates, we show that plates' vibrations become miniscule after the load is removed. We call this phenomenon as vibration attenuation. It is independent of the dwell time during which the load is a constant. We hypothesize that plates exhibit this phenomenon because nearly all of plate's strain energy is due to deformations corresponding to the fundamental bending mode of vibration. Thus taking the 1st bending mode shape of the plate vibration as the basis function, we reduce the problem to that of solving a single second-order ordinary differential equation. We show that this reduced-order model gives excellent results for monolithic and composite plates subjected to different loads. Rectangular plates studied in the 2nd problem have points on either one or two normals to their midsurface constrained from translating in all three directions. We find that deformations corresponding to several modes of vibration are annulled in a region of the plate divided by a plane through the constraining points; this phenomenon is termed mode localization. New results include: (i) the localization of both in-plane and out-of-plane modes of vibration, (ii) increase in the mode localization intensity with an increase in the length/width ratio of a rectangular plate, (iii) change in the mode localization characteristics with the fiber orientation angle in unidirectional fiber- reinforced laminae, (iv) mode localization due to points on two normals constrained, and (iv) the exchange of energy during forced harmonic vibrations between two regions separated by the line of nearly stationary points that results in a beating-like phenomenon in a sub-region of the plate. This technique can help design a structure with vibrations limited to its small sub-region, and harvesting energy of vibrations of the sub-region. In the third problem, we study finite transient deformations of rectangular plates using the TSNDT. The mathematical model includes all geometric and material nonlinearities. We compare the results of linear and nonlinear TSNDT FEM with the corresponding 3D FEM results from ABAQUS and note that the TSNDT is capable of predicting reasonably accurate results of displacements and in-plane stresses. However, the errors in computing transverse stresses are larger and the use of a two point stress recovery scheme improves their accuracy. We delineate the effects of nonlinearities by comparing results from the linear and the nonlinear theories. We observe that the linear theory over-predicts the deformations of a plate as compared to those obtained with the inclusion of geometric and material nonlinearities. We hypothesize that this is an effect of stiffening of the material due to the nonlinearity, analogous to the strain hardening phenomenon in plasticity. Based on this observation, we propose that the consideration of nonlinearities is essential in modeling plates undergoing large deformations as linear model over-predicts the deformation resulting in conservative design criteria. We also notice that unlike linear elastic plate bending, the neutral surface of a nonlinearly elastic bending plate, defined as the plane unstretched after the deformation, does not coincide with the mid-surface of the plate. Due to this effect, use of nonlinear models may be of useful in design of sandwich structures where a soft core near the mid-surface will be subjected to large in-plane stresses. Doctor of Philosophy

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2

Asdal, Bent. "Static and free vibration analysis of advanced composites using shear-deformable rectangular plate finite elements." Thesis, Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/80092.

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A comparison of rectangular finite elements based on a first order shear deformation plate theory and a refined higher order plate theory is presented. Special attention is given to the representation of transverse shear strain, the phenomenon of "shear locking", and the selection of the interpolating polynomial. Both C⁰ and C¹ continuity elements are represented; the elements range from: 3 or 5 DOF per node, and 12 - 27 DOF per element. Static and free vibration analysis of isotropic and laminated plates with thicknesses ranging from extremely thin to very thick are presented, along with a convergence study. The finite element results are compared with the exact plate theory solutions. Of the elements investigated, the modified refined higher order theory element exhibits the best overall behavior. Master of Science

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3

Saliba, H. T. "Free vibration analysis of non-rectangular quadrilateral plates." Thesis, University of Ottawa (Canada), 1986. http://hdl.handle.net/10393/5264.

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4

Alizadeh, Y. "Free vibration of partially supported plates and shells." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/10751.

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First-order transverse shear-deformation Mindlin theory has been used to predict the free vibration frequencies and modal shapes for isotropic, laminated and composite plates or shells. A finite element model based on the small deflection linear theory has been developed to obtain numerical solutions for this class of problems. The results for some of the degenerate cases are compared with other results available in the literature. These analyses involve a wide number of variables, namely; material properties, aspect ratios, support conditions and also radius to base ratio. The cracked base plates, shells and blades are idealized as partially supported models with varying support lengths. The effects of the detached base length on natural frequencies, modal shapes and nodal lines of these types of structures are investigated. Although the expected decrease in frequency with increase in the detached base length is observed almost for all modes it is seen that this behavior is very pronounced for higher modes in both plates and shells. Analysis also showed that the variation of the detached base length has a small effect on the natural frequencies of plates and shells with large aspect ratios ( b/a > 2, r/a > 2).

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5

Mochida, Yusuke. "Bounded Eigenvalues of Fully Clamped and Completely Free Rectangular Plates." The University of Waikato, 2007. http://hdl.handle.net/10289/2508.

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Exact solution to the vibration of rectangular plates is available only for plates with two opposite edges subject to simply supported conditions. Otherwise, they are analysed by using approximate methods. There are several approximate methods to conduct a vibration analysis, such as the Rayleigh-Ritz method, the Finite Element Method, the Finite Difference Method, and the Superposition Method. The Rayleigh-Ritz method and the finite element method give upper bound results for the natural frequencies of plates. However, there is a disadvantage in using this method in that the error due to discretisation cannot be calculated easily. Therefore, it would be good to find a suitable method that gives lower bound results for the natural frequencies to complement the results from the Rayleigh-Ritz method. The superposition method is also a convenient and efficient method but it gives lower bound solution only in some cases. Whether it gives upper bound or lower bound results for the natural frequencies depends on the boundary conditions. It is also known that the finite difference method always gives lower bound results. This thesis presents bounded eigenvalues, which are dimensionless form of natural frequencies, calculated using the superposition method and the finite difference method. All computations were done using the MATLAB software package. The convergence tests show that the superposition method gives a lower bound for the eigenvalues of fully clamped plates, and an upper bound for the completely free plates. It is also shown that the finite difference method gives a lower bound for the eigenvalues of completely free plates. Finally, the upper bounds and lower bounds for the eigenvalues of fully clamped and completely free plates are given.

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6

Kaul, Vibhu. "Free vibration analysis of continuous orthotropic plates and bridge decks." Thesis, University of Ottawa (Canada), 1986. http://hdl.handle.net/10393/4821.

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7

Ohman, Hans J. L. "Free vibration analysis of rectangular plates with internal point supports." Thesis, University of Ottawa (Canada), 1991. http://hdl.handle.net/10393/7492.

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Interest in the free vibration frequencies and associated mode shapes of rectangular plates resting on internal point supports has arisen in connection with the design of electronic circuit boards, solar panels and other industrial problems. An analytical solution is presented for the free vibration analysis of rectangular plates with multiple internal point supports. The solution is also shown to be easily modified to account for the effects of attached masses. The basic solution for each case consists of the Levy type solution for a plate with one discrete point support. N similar solutions for N discrete point supports are then superimposed to create an eigenvalue matrix from which the plate's natural frequencies and associated mode shapes can be determined. Due to the nature of the Levy type solution, only plates with two opposite edges simply supported are considered. The remaining edges are either simply supported, clamped or free. There are therefore six possible combinations of plate boundary conditions. The objective of this thesis is to give a concise and clear description of the mathematical procedure employed and to present the results of some representative frequency and mode shape studies.

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8

Fulford, Sarah Xochitl. "Analytical analysis of the free vibration of partially clamped cantilever plates." Thesis, University of Ottawa (Canada), 1994. http://hdl.handle.net/10393/6536.

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The method of superposition is used to analyze the free vibration of thin rectangular plates, partially clamped along one edge and free everywhere else. This study has been undertaken because of interest in the dynamic behaviour of electronic circuit boards which are sometimes given support of this nature. This problem is not known to have been studied before using an analytical type method. Eight building blocks are superimposed to obtain the final solution. Each building block is solved individually using the Levy-type solution. A detailed mathematical development of the solution is shown for each building block in dimensionless form. The natural frequencies and mode shapes for plates with varying aspect ratios and clamped lengths can be found using this method. Eigenvalues are shown to converge and tabulated values are given to at least three digit accuracy. Frequencies and mode shapes agree very well with experimentally found results and with results found using a commercially used finite element method software package.

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9

Nguyen, Khang V. "Free vibration analysis of rectangular orthotropic cantilever plates with point supports." Thesis, University of Ottawa (Canada), 1994. http://hdl.handle.net/10393/10365.

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The free vibration analysis of rectangular plates has been of interest to many scholars and practitioners over the years due to their wide range of applications. However, most of the studies involve the typical case of isotropy. A study has been done in the analysis of free vibration of orthotropic cantilever plates with internal point supports. The analysis makes use of the Superposition Method which, by superimposing appropriate building blocks, can provide "exact" analytical solution to this problem of orthotropy. In each case of symmetric and antisymmetric vibration modes under study, three different plate problems whose Levy-type solutions can be obtained, are superimposed. The constants in each solution, created during their boundary condition formulations, are adjusted in such a way so their combination would provide boundary conditions the same to those required for the cantilever plate. Upon superimposing, an eigenvalue matrix is created which allows the eigenvalues to be determined. Accuracy of the resultant eigenvalues is verified by recognising that the governing differential equation is satisfied exactly and that the required plate boundary conditions are satisfied to certain desired degree of exactitude. The objective of this thesis is to describe the necessary modifications to adapt the superposition method to orthotropic plate problems, and to show the mathematical procedures employed in the analysis. In addition, the results of some representative frequency and mode shape studies will be presented which include a wide range of plate geometries and various levels of orthotropy.

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10

Javanshir, Hasbestan Jaber. "Free Flexural (or Bending) Vibration Analysis Of Certain Of Stiffened Composite Plates Or Panels In Flight Vehicle Structures." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12611489/index.pdf.

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In this study, the &ldquo Free Flexural (or Bending) Vibrations of Stiffened Plates or Panels&rdquo are investigated in detail. Two different Groups of &ldquo Stiffened Plates&rdquo will be considered. In the first group, the &ldquo Type 4&rdquo and the &ldquo Type 6&rdquo of &ldquo Group I&rdquo of the &ldquo Integrally-Stiffened and/or Stepped-Thickness Plate or Panel Systems&rdquo are theoretically analyzed and numerically solved by making use of the &ldquo Mindlin Plate Theory&rdquo . Here, the natural frequencies and the corresponding mode shapes, up to the sixth mode, are obtained for each &ldquo Dynamic System&rdquo . Some important parametric studies are also presented for each case. In the second group, the &ldquo Class 2&rdquo and the &ldquo Class 3&rdquo of the &ldquo Bonded and Stiffened Plate or Panel Systems&rdquo are also analyzed and solved in terms of the natural frequencies with their corresponding mode shapes. In this case, the &ldquo Plate Assembly&rdquo is constructed by bonding &ldquo Stiffening Plate Strips&rdquo to a &ldquo Base Plate or Panel&rdquo by dissimilar relatively thin adhesive layers. This is done with the purpose of reinforcing the &ldquo Base Plate or Panel&rdquo by these &ldquo Stiffening Strips&rdquo in the appropriate locations, so that the &ldquo Base Plate or Panel&rdquo will exhibit satisfactory dynamic response. The forementioned &ldquo Bonded and Stiffened Systems&rdquo may also be used to repair a damaged (or rather cracked) &ldquo Base Plate or Panel&rdquo . Here in the analysis, the &ldquo Base Plate or Panel&rdquo , the &ldquo Stiffening Plate Strips&rdquo as well as the in- between &ldquo adhesive layers&rdquo are assumed to be linearly elastic continua. They are assumed to be dissimilar &ldquo Orthotropic Mindlin Plates&rdquo . Therefore, the effects of shear deformations and rotary moments of inertia are considered in the theoretical formulation. In each case of the &ldquo Group I&rdquo and &ldquo Group II&rdquo problems, the &ldquo Governing System of Dynamic Equations&rdquo for every problem is reduced to the &ldquo First Order Ordinary Differential Equations&rdquo . In other words the &ldquo Free Vibrations Problem&rdquo , in both cases, is an &ldquo Initial and Boundary Value Problem&rdquo is reduced to a &ldquo Two- Point or Multi-Point Boundary Value Problem&rdquo by using the present &ldquo Solution Technique&rdquo . For this purpose, these &ldquo Governing Equations&rdquo are expressed in &ldquo compact forms&rdquo or &ldquo state vector&rdquo forms. These equations are numerically integrated by the so-called &ldquo Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)&rdquo . In the numerical results, the mode shapes together with their corresponding non-dimensional natural frequencies are presented up to the sixth mode and for various sets of &ldquo Boundary Conditions&rdquo for each structural &ldquo System&rdquo . The effects of several important parameters on the natural frequencies of the aforementioned &ldquo Systems&rdquo are also investigated and are graphically presented for each &ldquo Stiffened and Stiffened and Bonded Plate or Panel System&rdquo . Additionally, in the case of the &ldquo Bonded and Stiffened System&rdquo , the significant effects of the &ldquo adhesive material properties&rdquo (i.e. the &ldquo Hard&rdquo adhesive and the &ldquo Soft&rdquo adhesive cases) on the dynamic response of the &ldquo plate assembly&rdquo are also presented.

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11

Kang, Lan. "Linear and non-linear free vibration analysis of plates and shallow shells." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0025/MQ30714.pdf.

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12

Alanbay, Berkan. "Free Vibrations and Static Deformations of Composite Laminates and Sandwich Plates using Ritz Method." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/103087.

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In this study, Ritz method has been employed to analyze the following problems: free vibrations of plates with curvilinear stiffeners, the lowest 100 frequencies of thick isotropic plates, free vibrations of thick quadrilateral laminates and free vibrations and static deformations of rectangular laminates, and sandwich structures. Admissible functions in the Ritz method are chosen as a product of the classical Jacobi orthogonal polynomials and weight functions that exactly satisfy the prescribed essential boundary conditions while maintaining orthogonality of the admissible functions. For free vibrations of plates with curvilinear stiffeners, made possible by additive manufacturing, both plate and stiffeners are modeled using a first-order shear deformation theory. For the thick isotropic plates and laminates, a third-order shear and normal deformation theory is used. The accuracy and computational efficiency of formulations are shown through a range of numerical examples involving different boundary conditions and plate thicknesses. The above formulations assume the whole plate as an equivalent single layer. When the material properties of individual layers are close to each other or thickness of the plate is small compared to other dimensions, the equivalent single layer plate (ESL) theories provide accurate solutions for vibrations and static deformations of multilayered structures. If, however, sufficiently large differences in material properties of individual layers such as those in sandwich structure that consists of stiff outer face sheets (e.g., carbon fiber-reinforced epoxy composite) and soft core (e.g., foam) exist, multilayered structures may exhibit complex kinematic behaviors. Hence, in such case, Cz0 conditions, namely, piecewise continuity of displacements and the interlaminar continuity of transverse stresses must be taken into account. Here, Ritz formulations are extended for ESL and layerwise (LW) Nth-order shear and normal deformation theories to model sandwich structures with various face-to-core stiffness ratios. In the LW theory, the C0 continuity of displacements is satisfied. However, the continuity of transverse stresses is not satisfied in both ESL and LW theories leading to inaccurate transverse stresses. This shortcoming is remedied by using a one-step well-known stress recovery scheme (SRS). Furthermore, analytical solutions of three-dimensional linear elasticity theory for vibrations and static deformations of simply supported sandwich plates are developed and used to investigate the limitations and applicability of ESL and LW plate theories for various face-to-core stiffness ratios. In addition to natural frequency results obtained from ESL and LW theories, the solutions of the corresponding 3-dimensional linearly elastic problems obtained with the commercial finite element method (FEM) software, ABAQUS, are provided. It is found that LW and ESL (even though its higher-order) theories can produce accurate natural frequency results compared to FEM with a considerably lesser number of degrees of freedom. Doctor of Philosophy In everyday life, plate-like structures find applications such as boards displaying advertisements, signs on shops and panels on automobiles. These structures are typically nailed, welded, or glued to supports at one or more edges. When subjected to disturbances such as wind gusts, plate-like structures vibrate. The frequency (number of cycles per second) of a structure in the absence of an applied external load is called its natural frequency that depends upon plate's geometric dimensions, its material and how it is supported at the edges. If the frequency of an applied disturbance matches one of the natural frequencies of the plate, then it will vibrate violently. To avoid such situations in structural designs, it is important to know the natural frequencies of a plate under different support conditions. One would also expect the plate to be able to support the designed structural load without breaking; hence knowledge of plate's deformations and stresses developed in it is equally important. These require mathematical models that adequately characterize their static and dynamic behavior. Most mathematical models are based on plate theories. Although plates are three-dimensional (3D) objects, their thickness is small as compared to the in-plane dimensions. Thus, they are analyzed as 2D objects using assumptions on the displacement fields and using quantities averaged over the plate thickness. These provide many plate theories, each with its own computational efficiency and fidelity (the degree to which it reproduces behavior of the 3-D object). Hence, a plate theory can be developed to provide accurately a quantity of interest. Some issues are more challenging for low-fidelity plate theories than others. For example, the greater the plate thickness, the higher the fidelity of plate theories required for obtaining accurate natural frequencies and deformations. Another challenging issue arises when a sandwich structure consists of strong face-sheets (e.g., made of carbon fiber-reinforced epoxy composite) and a soft core (e.g., made of foam) embedded between them. Sandwich structures exhibit more complex behavior than monolithic plates. Thus, many widely used plate theories may not provide accurate results for them. Here, we have used different plate theories to solve problems including those for sandwich structures. The governing equations of the plate theories are solved numerically (i.e., they are approximately satisfied) using the Ritz method named after Walter Ritz and weighted Jacobi polynomials. It is shown that these provide accurate solutions and the corresponding numerical algorithms are computationally more economical than the commonly used finite element method. To evaluate the accuracy of a plate theory, we have analytically solved (i.e., the governing equations are satisfied at every point in the problem domain) equations of the 3D theory of linear elasticity. The results presented in this research should help structural designers.

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13

Michelussi, David J. "Free vibration and buckling analysis of thin rectangular plates with classical boundary conditions under unilateral in-plane loads." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/mq20937.pdf.

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14

Yeilaghi, Tamijani Ali. "Vibration and Buckling Analysis of Unitized Structure Using Meshfree Method and Kriging Model." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/37817.

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The Element Free Galerkin (EFG) method, which is based on the Moving Least Squares (MLS) approximation, is developed here for vibration, buckling and static analysis of homogenous and FGM plate with curvilinear stiffeners. Numerical results for different stiffeners configurations and boundary conditions are presented. All results are verified using the commercial finite element software ANSYSÂ® and other available results in literature. In addition, the vibration analysis of plates with curvilinear stiffeners is carried out using Ritz method. A 24 by 28 in. curvilinear stiffened panel was machined from 2219-T851 aluminum for experimental validation of the Ritz and meshfree methods of vibration mode shape predictions. Results were obtained for this panel mounted vertically to a steel clamping bracket using acoustic excitation and a laser vibrometer. Experimental results appear to correlate well with the meshfree and Ritz method results. In reality, many engineering structures are subjected to random pressure loads in nature and cannot be assumed to be deterministic. Typical engineering structures include buildings and towers, offshore structures, vehicles and ships, are subjected to random pressure. The vibrations induced from gust loads, engine noise, and other auxiliary electrical system can also produce noise inside aircraft. Consequently, all flight vehicles operate in random vibration environment. These random loads can be modeled by using their statistical properties. The dynamical responses of the structures which are subjected to random excitations are very complicated. To investigate their dynamic responses under random loads, the meshfree method is developed for random vibration analysis of curvilinearly-stiffened plates . Since extensive efforts have been devoted to study the buckling and vibration analysis of stiffened panel to maximize their natural frequencies and critical buckling loads, these structures are subjected to in-plane loading while the vibration analysis is considered. In these cases the natural frequencies calculated by neglecting the in-plane compression are usually over predicted. In order to have more accurate results it might be necessary to take into account the effects of in-plane load since it can change the natural frequency of plate considerably. To provide a better view of the free vibration behavior of the plate with curvilinear stiffeners subjected to axial/biaxial or shear stresses several numerical examples are studied. The FEM analysis of curvilinearly stiffened plate is quite computationally expensive, and the meshfree method seems to be a proper substitution to reduce the CPU time. However it will still require many simulations. Because of the number of simulations may be required in the solution of an engineering optimization problem, many researchers have tried to find approaches and techniques in optimization which can reduce the number of function evaluations. In these problems, surrogate models for analysis and optimization can be very efficient. The basic idea in surrogate model is to reduce computational cost and giving a better understanding of the influence of the design variables on the different objectives and constrains. To use the advantage of both meshfree method and surrogate model in reducing CPU time, the meshfree method is used to generate the sample points and combination of Kriging (a surrogate model) and Genetic Algorithms is used for design of curvilinearly stiffened plate. The meshfree and kriging results and CPU time were compared with those obtained using EBF3PanelOpt. Ph. D.

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15

Shih, Hoi Wai. "Damage assessment in structures using vibration characteristics." Thesis, Queensland University of Technology, 2009. https://eprints.qut.edu.au/30319/1/Hoi_Shih_Thesis.pdf.

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Changes in load characteristics, deterioration with age, environmental influences and random actions may cause local or global damage in structures, especially in bridges, which are designed for long life spans. Continuous health monitoring of structures will enable the early identification of distress and allow appropriate retrofitting in order to avoid failure or collapse of the structures. In recent times, structural health monitoring (SHM) has attracted much attention in both research and development. Local and global methods of damage assessment using the monitored information are an integral part of SHM techniques. In the local case, the assessment of the state of a structure is done either by direct visual inspection or using experimental techniques such as acoustic emission, ultrasonic, magnetic particle inspection, radiography and eddy current. A characteristic of all these techniques is that their application requires a prior localization of the damaged zones. The limitations of the local methodologies can be overcome by using vibration-based methods, which give a global damage assessment. The vibration-based damage detection methods use measured changes in dynamic characteristics to evaluate changes in physical properties that may indicate structural damage or degradation. The basic idea is that modal parameters (notably frequencies, mode shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Changes in the physical properties will therefore cause changes in the modal properties. Any reduction in structural stiffness and increase in damping in the structure may indicate structural damage. This research uses the variations in vibration parameters to develop a multi-criteria method for damage assessment. It incorporates the changes in natural frequencies, modal flexibility and modal strain energy to locate damage in the main load bearing elements in bridge structures such as beams, slabs and trusses and simple bridges involving these elements. Dynamic computer simulation techniques are used to develop and apply the multi-criteria procedure under different damage scenarios. The effectiveness of the procedure is demonstrated through numerical examples. Results show that the proposed method incorporating modal flexibility and modal strain energy changes is competent in damage assessment in the structures treated herein.

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16

Shih, Hoi Wai. "Damage assessment in structures using vibration characteristics." Queensland University of Technology, 2009. http://eprints.qut.edu.au/30319/.

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Changes in load characteristics, deterioration with age, environmental influences and random actions may cause local or global damage in structures, especially in bridges, which are designed for long life spans. Continuous health monitoring of structures will enable the early identification of distress and allow appropriate retrofitting in order to avoid failure or collapse of the structures. In recent times, structural health monitoring (SHM) has attracted much attention in both research and development. Local and global methods of damage assessment using the monitored information are an integral part of SHM techniques. In the local case, the assessment of the state of a structure is done either by direct visual inspection or using experimental techniques such as acoustic emission, ultrasonic, magnetic particle inspection, radiography and eddy current. A characteristic of all these techniques is that their application requires a prior localization of the damaged zones. The limitations of the local methodologies can be overcome by using vibration-based methods, which give a global damage assessment. The vibration-based damage detection methods use measured changes in dynamic characteristics to evaluate changes in physical properties that may indicate structural damage or degradation. The basic idea is that modal parameters (notably frequencies, mode shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Changes in the physical properties will therefore cause changes in the modal properties. Any reduction in structural stiffness and increase in damping in the structure may indicate structural damage. This research uses the variations in vibration parameters to develop a multi-criteria method for damage assessment. It incorporates the changes in natural frequencies, modal flexibility and modal strain energy to locate damage in the main load bearing elements in bridge structures such as beams, slabs and trusses and simple bridges involving these elements. Dynamic computer simulation techniques are used to develop and apply the multi-criteria procedure under different damage scenarios. The effectiveness of the procedure is demonstrated through numerical examples. Results show that the proposed method incorporating modal flexibility and modal strain energy changes is competent in damage assessment in the structures treated herein.

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17

Ding, Wei. "Free vibration studies of shear deformable plates by the traditional superposition and Superposition-Galerkin method." Thesis, University of Ottawa (Canada), 1995. http://hdl.handle.net/10393/9522.

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In the first part of the present study, it is demonstrated that the traditional superposition method lends itself successfully to obtaining of eigenvalues and mode shapes for completely free shear deformable plates, namely, the thick isotropic plates and symmetric cross-ply laminated plates. The effect of transverse shear deformation is taken into account by means of the first order shear deformation relationship as developed by Mindlin. The governing differential equations are satisfied exactly throughout the plate domain and free edge boundary conditions are satisfied to any desired degree of accuracy. These appear to be the first accurate solutions to these important completely free plate vibration problems. Subsequently, a new modified Superposition-Galerkin method is developed for analyzing the free vibration problem of symmetric cross-ply plates with any combination of clamped and simply supported boundary conditions. It is shown that this new approach leads to vast simplification of computational procedures in comparison to the traditional superposition method. Nevertheless it is seen that excellent agreement is achieved when results obtained by the Galerkin-Superposition method are compared with those generated by previous researchers. It is expected that this new modified method will have application to various families of laminated plate vibration problems.

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18

Koduru, Hari Kishan. "Effects of rotational elastic edge supports on buckling and free vibration of thin rectangular plates." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0003/MQ46586.pdf.

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19

Li, Qian. "Three-dimensional analysis of functionally graded material plates, free vibration in thermal environment and thermal buckling." Thesis, University of Macau, 2008. http://umaclib3.umac.mo/record=b1783646.

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20

Fazzolari, Fiorenzo A. "Advanced dynamic stiffness formulations for free vibration and buckling analysis of laminated composite plates and shells." Thesis, City University London, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.635315.

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In this thesis both static and dynamic analyses of composite thin-walled structures are carried out. Most notably, the Dynamic Stiffness Method (DSM) has been extensively exploited to develop advanced formulations for plates and shells. In particular, the. Dynamic Stiffness (DS) matrices have been developed for laminated composite plates and shells using Higher-order Shear Deformation Theory (HSDT) in order to investigate their free vibration behavior and buckling characteristics. First, the Governing Differential Equations (GDEs) of motion and associated natural Boundary Conditions (BCs) (Neumann-type) for the given displacement field are derived via Hamilton's principle for both composite plate and shell structures. In the case of composite plates, the DS matrices are formulated for both out-of-plane and in-plane deformations. The GDEs for each of the two cases are solved in Levy's form separately. Next the problems for both plates and shells are reduced to a system of ordinary differential equations which are then solved by using the classical exponential solution procedure.

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21

Cil, Kursad. "Free Flexural (or Bending) Vibrations Analysis Of Doubly Stiffened, Composite, Orthotropic And/or Isotropic Base Plates And Panels (in Aero-structural Systems)." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/2/1062256/index.pdf.

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In this Thesis, the problem of the Free Vibrations Analysis of Doubly Stiffened Composite, Orthotropic and/or Isotropic, Base Plates or Panels (with Orthotropic Stiffening Plate Strips) is investigated. The composite plate or panel system is made of an Orthotropic and/or Isotropic Base Plate stiffened or reinforced by adhesively bonded Upper and Lower Orthotropic Stiffening Plate Strips. The plates are assumed to be the Mindlin Plates connected by relatively very thin adhesive layers. The general problem under study is considered in terms of three problems, namely Main PROBLEM I Main PROBLEM II and Main PROBLEM III. The theoretical formulation of the Main PROBLEMS is based on a First Order Shear Deformation Plate Theory (FSDPT) that is, in this case, the Mindlin Plate Theory. The entire composite system is assumed to have simple supports along the two opposite edges so that the Classical Levy&#039 s Solutions can be applied in that direction. Thus, the transverse shear deformations and the rotary moments of inertia of plates are included in the formulation. The very thin, yet elastic deformable adhesive layers are considered as continua with transverse normal and shear stresses. The damping effects in the plates and the adhesive layers are neglected. The sets of the systems of equations of the Mindlin Plate Theory are reduced to a set of the Governing System of First Order Ordinary Differential Equations in the state vector form. The sets of the Governing System for each Main PROBLEM constitute a Two-Point Boundary Value Problem in the y-direction which is taken along the length of the plates. Then, the system is solved by the Modified Transfer Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials)which is a relatively semi-analytical and numerical technique. The numerical results and important parametric studies of the natural modes and the corresponding frequencies of the composite system are presented.

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Qi, Hai. "Free vibration analysis of rectangular Mindlin plates resting on uniform elastic edge supports by the superposition method." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/mq20943.pdf.

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Stangier, Stefanie D. "Theoretical and experimental investigation of the free vibration of parallelogram plates with simply supported and clamped boundary conditions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq28462.pdf.

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Yuan, Lisha. "Optimum First Failure Loads of Sandwich Plates/Shells and Vibrations of Incompressible Material Plates." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/102664.

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Due to high specific strength and stiffness as well as outstanding energy-absorption characteristics, sandwich structures are extensively used in aircraft, aerospace, automobile, and marine industries. With the objective of finding lightweight blast-resistant sandwich structures for protecting infrastructure, we have found, for a fixed areal mass density, one- or two-core doubly-curved sandwich shell's (plate's) geometries and materials and fiber angles of unidirectional fiber-reinforced face sheets for it to have the maximum first failure load under quasistatic (blast) loads. The analyses employ a third-order shear and normal deformable plate/shell theory (TSNDT), the finite element method (FEM), a stress recovery scheme (SRS), the Tsai-Wu failure criterion and the Nest-Site selection (NeSS) optimization algorithm, and assume the materials to be linearly elastic. For a sandwich shell under the spatially varying static pressure on the top surface, the optimal non-symmetric one-core (two-core) design improves the first failure load by approximately 33% (27%) and 50% (36%) from the corresponding optimal symmetric design with clamped and simply-supported edges, respectively. For a sandwich plate under blast loads, it is found that the optimal one-core design is symmetric about the mid-surface with thick face sheets, and the optimal two-core design has a thin middle face sheet and thick top and bottom face sheets. Furthermore, the transverse shear stresses (in-plane transverse axial stresses) primarily cause the first failure in a core (face sheet). For the computed optimal design under a blast load, we also determined the collapse load by using the progressive failure analysis that degrades all elasticities of the failed material point to very small values. The collapse load of the clamped (simply-supported) sandwich structure is approximately 15%–30% (0%–17%) higher than its first failure load. Incompressible materials such as rubbers, polymers, and soft tissues that can only undergo volume preserving deformations have numerous applications in engineering and biomedical fields. Their vibration characteristics are important for using them as wave reflectors at interfaces with a fiber-reinforced sheet. In this work we have numerically analyzed free vibrations of plates made of a linearly elastic incompressible rubber-like material (Poison's ratio = 0.5) by using a TSNDT for incompressible materials and the mixed FEM. The displacements at nodes of a 9-noded quadrilateral element and the hydrostatic pressure at four interior nodes are taken as unknowns. Computed results are found to match well with the corresponding either analytical or numerical ones obtained with the commercial FE software Abaqus and the 3-dimensional linear elasticity theory. The analysis discerns plate's in-plane vibration modes. It is found that a simply supported plate admits more in-plane modes than the corresponding clamped and clamped-free plates. Doctor of Philosophy A simple example of a sandwich structure is a chocolate ice cream bar with the chocolate layer replaced by a stiff plate. Another example is the packaging material used to protect electronics during shipping and handling. The intent is to find the composition and the thickness of the "chocolate layer" so that the ice cream bar will not shatter when dropped on the floor. The objective is met by enforcing the chocolate layer with carbon fibers and then finding fiber materials, their alignment, ice cream or core material, and its thickness to resist anticipated loads with a prescribed level of certainty. Thus, a sandwich structure is usually composed of a soft thick core (e.g., foam) bonded to two relatively stiff thin skins (e.g., made of steel, fiber-reinforced composite) called face sheets. They are lightweight, stiff, and effective in absorbing mechanical energy. Consequently, they are often used in aircraft, aerospace, automobile, and marine industries. The load that causes a point in a structure to fail is called its first failure load, and the load that causes it to either crush or crumble is called the ultimate load. Here, for a fixed areal mass density (mass per unit surface area), we maximize the first failure load of a sandwich shell (plate) under static (dynamic) loads by determining its geometric dimensions, materials and fiber angles in the face sheets, and the number (one or two) of cores. It is found that, for a non-uniformly distributed static pressure applied on the central region of a sandwich shell's top surface, an optimal design that has different materials for the top and the bottom face sheets improves the first failure load by nearly 30%-50% from that of the optimally designed structure with identical face sheets. For the structure optimally designed for the first failure blast load, the ultimate failure load with all of its edges clamped (simply supported) is about 15%-30% (0%-17%) higher than its first failure load. This work should help engineers reduce weight of sandwich structures without sacrificing their integrity and save on materials and cost. Rubberlike materials, polymers, and soft tissues are incompressible since their volume remains constant when they are deformed. Plates made of incompressible materials have a wide range of applications in everyday life, e.g., we hear because of vibrations of the ear drum. Thus, accurately predicting their dynamic behavior is important. A first step usually is determining natural frequencies, i.e., the number of cycles of oscillations per second (e.g., a human heart beats at about 1 cycle/sec) completed by the structure in the absence of any externally applied force. Here, we numerically find natural frequencies and mode shapes of rubber-like material rectangular plates with different supporting conditions at the edges. We employ a plate theory that reduces a 3-dimensional (3-D) problem to a 2-D one and the finite element method. The problem is challenging because the incompressibility constraint requires finding the hydrostatic pressure as a part of the problem solution. We show that the methodology developed here provides results that match well with the corresponding either analytical or numerical solutions of the 3-D linear elasticity equations. The methodology is applicable to analyzing the dynamic response of composite structures with layers of incompressible materials embedded in it.

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Labaki, Wassim. "Computation of free vibration frequencies and mode shapes of cantilever plates with finite discontinuities in properties moving outward from the clamped edge." Thesis, University of Ottawa (Canada), 2001. http://hdl.handle.net/10393/8988.

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The study of rectangular cantilever plates with step discontinuities in properties is of interest in many areas of industry. Cantilever plates are assigned different properties to represent change in stiffness and mass creating therefore the concept of step discontinuities in properties. The step discontinuity in properties is best represented by dividing the cantilever plate into separate segments called spans, with each span having its own stiffness and/or mass distribution as one moves outwards from the clamped edge. This thesis presents the concept of dividing the cantilever plate into spans and provides accurate analytical solutions for free vibration frequencies and mode shapes. Chapter 1 introduces the reader to the theory of rectangular plates while chapter 2 concentrates on introducing the general solutions as applied to rectangular plates. Although there is no limit to the number of plate spans to be studied, three and four span cantilever plates were analysed in chapter 3. The computed eigenvalues are validated against previously published uniform rectangular cantilever plate free vibration results. They were found converging to the known values. Free vibration eigenvalues and mode shapes are then calculated for a variety of cantilever plates of different aspect ratios and with different span thicknesses creating a discontinuity in mass and flexural rigidity along the plate. The results are presented in chapter 4 and discussed in chapter 5.

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Ahmad, Naveed. "Passive Damping in Stiffened Structures Using Viscoelastic Polymers." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/79566.

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Noise and vibration suppression is an important aspect in the design process of structures and machines. Undesirable vibrations can cause fatigue in a structure and are, therefore, a risk to the safety of a structure. One of the most effective and widely used methods of mitigating these unwanted vibrations from a system is passive damping, by using a viscoelastic material. This dissertation will primarily focus on constrained layer passive damping treatments in structures and the investigation of associated complex modes. The key idea behind constrained damping treatment is to increase damping as affected by the presence of a highly damped core layer vibrating mainly in shear. Our main goal was to incorporate viscoelastic material in a thick stiffened panel with plate-strip stiffeners, to enhance the damping characteristics of the structure. First, we investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the principle of virtual work, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the viscoelastic material was modeled using the complex modulus approach. We used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, by including complex modulus in the base and constraining layers. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically damped and non-proportionally damped structures. Secondly, we studied the free vibration response of an integrally stiffened and/or stepped plate. The stiffeners used here were plate-strip stiffeners, unlike the rib stiffeners often investigated by researchers. Both plate and stiffeners were analyzed using the first-order shear deformation theory. The deflections and rotations were assumed as a product of Timoshenko beam functions, chosen appropriately according to the given boundary conditions. Unlike Navier and Levy solution techniques, the approach used here can also be applied to fully clamped, free and cantilever supported stiffened plates. The governing differential equations were solved using the Rayleigh-Ritz method. The development of the stiffness and the mass matrices in the Ritz analysis was found to consume a huge amount of CPU time due to the recursive integration of Timoshenko beam functions. An approach is suggested to greatly decrease this amount of CPU time, by replacing the recursive integration in a loop structure in the computer program, with the analytical integration of the integrand in the loop. The numerical results were compared with the exact solutions available in the literature and the commercially available finite-element software ABAQUS. Some parametric studies were carried out to show the influence of certain important parameters on the overall natural frequencies of the stiffened plate. Finally, we investigated the damped response of an adhesively bonded plate employing plate-strip stiffeners, using FSDT for both the plate and stiffeners. The problem was analyzed using the principle of virtual work. At first, we did not consider damping in the adhesive in order to validate our code, by comparing our results with those available in the literature as well as with the results obtained using ABAQUS 3D model. The results were found to be highly satisfactory. We also considered the effect of changing the stiffness of the adhesive layer on the vibration of the bonded system. As a second step, we included damping in the stiffened structure using complex modulus approach, a widely used technique to represent the rheology of the viscoelastic material. We observed an overall increase in the natural frequencies of the system, due to the damping provided by the viscoelastic material. Moreover, it was noticed that when the thickness of the adhesive layer is increased, the natural frequencies and loss factor of the stiffened structure decrease. A viscoelastic material with high loss factor and small thickness will be a perfect design variable to obtain overall high damping in the structure. Ph. D.

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Karasin, Abdulhalim. "An Improved Finite Grid Solution For Plates On Generalized Foundations." Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12604697/index.pdf.

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In many engineering structures transmission of vertical or horizontal forces to the foundation is a major challenge. As a first approach to model it may be assumed that the foundation behaves elastically. For generalized foundations the model assumes that at the point of contact between plate and foundation there is not only pressure but also moments caused by interaction between the springs. In this study, the exact stiffness, geometric stiffness and consistent mass matrices of the beam element on two-parameter elastic foundation are extended to solve plate problems. Some examples of circular and rectangular plates on two-parameter elastic foundation including bending, buckling and free vibration problems were solved by the finite grid solution. Comparison with known analytical solutions and other numerical solutions yields accurate results.

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Sakanaka, Sandra Hiromi. "Determinação de frequencias naturais e cargas criticas em placas incluindo o efeito da deformação por cortante com o metodo dos elementos de contorno." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/257772.

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Orientador: Leandro Palermo Jr Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo Made available in DSpace on 2018-08-09T15:27:34Z (GMT). No. of bitstreams: 1 Sakanaka_SandraHiromi_M.pdf: 2300706 bytes, checksum: bf530823f185b6dbee7f56dd83d01a67 (MD5) Previous issue date: 2006 Resumo: A análise de vibração livre e de instabilidade de placas finas e placas moderadamente espessas é apresentada através do método dos elementos de contorno (MEC) considerando o efeito da deformação pela força cortante e, particularmente para o cálculo de freqüências naturais, o efeito da inércia rotatória é também considerado. A formulação da solução fundamental é baseada na teoria de Mindlin (1951) mas resultados para a teoria de Kirchhoff (1850) também podem ser obtidos [Palermo Jr. (2000)]. O presente trabalho usa a técnica da iteração inversa através do coeficiente de Rayleigh para a determinação das menores freqüências naturais e cargas críticas de instabilidade das placas. A implementação numérica emprega elementos de contorno isoparamétricos lineares contínuos e descontínuos. Elementos constantes de domínio são usados. Os parâmetros nodais são posicionados nos extremos dos elementos e os pontos de carregamento dos elementos descontínuos são deslocados para o interior a uma distância igual a um quarto do comprimento do elemento. Expressões analíticas das integrais de contorno são desenvolvidas para os casos em que o elemento contém o ponto de carregamento e integração numérica de Gauss-Legendre é feita nos outros casos. As integrais de domínio foram transformadas em integrais de contorno para cada célula e foram tratadas como cargas de superfície atualizadas através de um processo iterativo. Os resultados obtidos foram comparados com valores encontrados na literatura para demonstrar a precisão do presente trabalho Abstract: Free-vibration analysis and static buckling loads analysis of thin and thick plates considering the shear deformation effects using the Boundary Element Method (BEM) is presented. For the calculation of natural frequencies, the rotatory inertia is also counted. The formulation of the fundamental solution considers Mindlin¿s plates but results according to the classic theory can also be obtained [Palermo Jr. (2000)]. The present article makes use of the inverse iteration with Rayleigh coefficient to determine the smallest natural frequencies and the smallest static buckling loads of the plates. The numerical implementation employed continuous or discontinuous isoparametric linear boundary elements according to the characteristics of the problem to be solved. Constant domain elements are used. Nodal parameters have been placed at the ends of the elements and the source point of the discontinuous elements were positioned at a distance equal to one quarter of the element length. Analytical expressions have been employed in the integration on elements containing the source point and Gauss-Legendre numerical integration scheme otherwise. The domain integrals containing the inertia effects or nonlinear effect have been transformed into boundary integrals for each cell and were treated as surface loads updated in an iterative process. The obtained results were compared to those in literature to demonstrate the precision of this proposal Mestrado Estruturas Mestre em Engenharia Civil

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Huang, Chiung-shiann. "Singularities in plate vibration problems /." The Ohio State University, 1991. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487688507503742.

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URRACI, ANDREA. "Development of accurate and efficient structural models for analysis of multilayered and sandwich structures of industrial interest." Doctoral thesis, Politecnico di Torino, 2020. http://hdl.handle.net/11583/2829677.

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Rosen, Oren. "Sturm-Liouville extensions : applications in plate vibration /." Diss., Digital Dissertations Database. Restricted to UC campuses, 2006. http://uclibs.org/PID/11984.

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Bercin, A. N. "High frequency vibration analysis of plate structures." Thesis, Cranfield University, 1993. http://dspace.lib.cranfield.ac.uk/handle/1826/10030.

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Noise and vibration are important design issues for many types of vehicles such as ships, cars, and aeroplanes. Structure borne sound, which may be of relatively high frequency, usually emanates from an engine or some other type of localised source and propagates through the vehicle. Excessive vibration levels, and thus structural damage, may occur while structural acoustic interactions may lead to unacceptable interior noise. In the analysis of energy transmission between plate structures, it is common practice to consider only bending modes (or waves) of the structure. However if the concern is with high frequency vibration analysis, then due allowance may need to be made for the presence of inplane shear and longitudinal modes. Due to the infeasibility of the industry standard technique, the Finite Element Method, at high frequencies, almost all of the studies that have investigated the importance of in-plane energy transmission have used Statistical Energy Analysis (SEA). In this study an existing dynamic stiffness method is extended to include in-plane effects, and used as a benchmark against which SEA is assessed. Additionally the Wave Intensity Analysis (WIA) technique, which is an improved form of SEA, is extended to in-plane vibrations, and used to identify some of the reasons for the poor performance of SEA in certain applications. All three methods are applied to a wide range of plate structures within the frequency range of 600 Hz to 20 kHz. While the response levels as predicted by the WIA are generally quite close to exact results, it has been found that although all of the requirements which are usually postulated for the successful application of SEA are fulfilled, SEA severely underpredicts the energy transmission in large structures because of the diffuse wave field assumption. It is also shown that the exclusion of in-plane modes may lead to sizeable errors in energy predictions unless the structure is very simple.

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Hanna, Nagy F. "Thick plate theories, with applications to vibration /." The Ohio State University, 1991. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487683049374286.

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Reinhard, Moritz. "Free elastic plate impact into water." Thesis, University of East Anglia, 2013. https://ueaeprints.uea.ac.uk/47926/.

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The Wagner theory, developed 80 years ago, is an analytical method for solving problems where a body with small deadrise angle impacts onto an undisturbed water surface of infinite depth. In this study, two-dimensional impact models based on the Wagner theory are developed which account for the elasticity of the body, for large horizontal speed of the body and flow separation from the body. In chapter 3, the problems of inclined rigid and elastic plates, impacting the fluid vertically, are solved. The elastic plate deflection is governed by Euler’s beam equation, subject to free-free boundary conditions. In chapter 4 and 5, impact problems of rigid and elastic plates and blunt bodies with high horizontal speed are considered. A smooth separation of the free surface flow from the body is imposed by Kutta’s condition and the Brillouin-Villat condition. In chapter 6, we account for fluid separation from the body in the free vertical fall of a rigid plate and a blunt body. In all problems considered in this thesis, the rigid and elastic plate motions, the fluid flow, and the positions of the turnover regions and the separation points are coupled. We found that hydrodynamic forces on an elastic body can be significantly different from those on a rigid body. In particular, the elasticity of the body can promote cavitation and ventilation. It is shown that horizontal speed of the body increases the hydrodynamic forces on the body and the jet energy significantly. For free-fall problems at high horizontal speed, the body can exit the fluid after entering if the forward speed is large enough. It is illustrated that the hydrodynamic forces on the body and the motion of the body strongly depend on the separation model. For the Brillouin-Villat separation criterion, we found that the position of the separation point is sensitive to the body vibration.

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Naderian, Hamidreza. "Advanced Numerical Techniques for Dynamic and Aerodynamic Analysis of Bridges." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36089.

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To meet the economic, social and infrastructure needs of the community for safe and efficient transportation systems, long span bridges have been built throughout the world. Long span bridges are one of the most challenging kinds of structures in civil engineering. The cable-stayed bridges are of great interest mainly as an alternative and a more economic solution than the one of suspension bridges. In addition, the fiber reinforced polymer (FRP) composites are, nowadays, successfully used for constructing modern bridges, where the significant weight saving provides additional benefits. Because of the great flexibility, modern long-span cable-stayed bridges are usually very susceptible to dynamic loads especially to the earthquake and strong winds. Therefore, the earthquake-resistant and wind-resistant designs become one of key issues for successful construction of bridges. The objective of the present research is to develop a very efficient spline finite strip technique, for modelling and analysis of both conventional and hybrid FRP cable-stayed bridges. The study falls into the categories of bending, free vibration, seismic, and aerodynamic flutter analysis. The spline finite strip method (SFSM) is one of the most efficient numerical methods for structural analysis of bridges, reducing the time required for estimating the structural response without affecting the degree of accuracy. In the finite strip method, the degrees of freedom could be significantly reduced due to the semi-analytical nature of this method. However, the previous versions of SFSM are not able to model the entire bridge system. For that reason, the structural interactions between different structural components of the bridge could not be handled. In addition, the vibrations and displacements of the towers and cables could not be investigated. In the present formulation, all these obstacles have been eliminated. Moreover, the proposed finite strip technique is very efficient and accurate due to the drastic reduction in the formulation time, simplicity of data preparation, rapid rate convergence of the results, and the semi-analytical nature. Last but not least, and for the first time, a fully finite strip solution is extended to the area of wind engineering. Using the spline finite strip discretization, the aerodynamic stiffness and mass properties of the long-span cable-stayed bridge are derived. The aerodynamic properties along with the structural properties of long-span plates and bridges are formulated in the aerodynamic equation of motion and are used to analyze the flutter problem. The accuracy and efficiency of the proposed advanced finite strip method is verified against the finite element and field measurement results. The results demonstrate that this methodology and the associated computer code can accurately predict the dynamic and aerodynamic responses of the conventional and FRP long-span cable-stayed bridge systems. The outcome of the present research will lead to a comprehensive structural analysis of bridges in the framework of the proposed discretization which is more efficient and straightforward than the finite element analysis.

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Chen, Yao-Pang, and 陳耀邦. "Free vibration analysis of delaminated sandwich beam-plate." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/03806763448048016618.

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碩士 國立成功大學 航空太空工程學系 86 Abstract:The effect of delamination on the natural frequency of a delaminated sandwich beam was investigated by Finite Element Method. Bending theory of sandwich beams were employed for the analysis. The deflection due to bending and shear of sandwich beams were described by a third order polynomial.. The effect of delamination length, delamination location, thickness ratio of face to core, boundary condition and material properties were studied. Results show that beam with longer delamination, the vibration mode tends to be local.

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Wen-YuLiang and 梁文宇. "Axisymmetric Free Vibration of Transversely Isotropic Circular Plate." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/95425663704912517736.

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碩士 國立成功大學 土木工程學系碩博士班 98 On the basis of the state space approach, the axisymmetric free vibration of transversely isotropic circular plate is analyzed. The state equation of axisymmetric free vibration of transversely isotropic circular plate is established from three-dimensional basic equations of elasticity in the cylindrical coordinates. By using separation of variables, the components of displacements and stresses are expressed as a superposition of two sets of particular solutions of the state equation with enough coefficients to satisfy arbitrary boundary conditions and determine the frequencies for the free vibration of plate. The results for the transversely isotropic and the isotropic plates are presented, and the latter are compared with those based on the linear shear-deformation Mindlin plate theory.

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Jena, Rini. "Free Vibration and Buckling Analysis of Sandwich Plate." Thesis, 2016. http://ethesis.nitrkl.ac.in/9201/1/2016_MT_RJena.pdf.

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The present study deals with the free vibration analysis of a three layered sandwich plate. It consists of a damping layer which is viscoelastic in nature being sandwiched or glued in between two elastic face plates; one being the basic plate at the bottom and another one is the constraining layer at the top. The finite element modeling is based on first order shear deformation theory. The mathematical calculation is done by Finite Element Method in which each layer of the plate is discretized into small elements and by using the governing equations of motion, the static and dynamic characteristics of a sandwich plate like its frequency and its buckling load capacity is determined. Here we have a four-noded sandwich plate element which has seven degrees of freedom at each node in order to have same transverse displacement. The equations of motion are determined by Hamilton’s principle. Then the required validation is done by comparing the results of the theoretical method with those obtained from analysis using ANSYS. The analysis is done by using ANSYS (APDL) software and its natural frequencies and their nodal displacements were found out by taking simply supported end condition on all the four sides of a sandwich plate. For studying the buckling analysis of plates, a uniaxial compressive load was applied on the edge and the effect of various geometric parameters on critical buckling load was determined. The convergence of buckling load with mesh size was studied .The results obtained were same as the reference values with good accuracy.

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Hung, Wei-peng, and 洪惟鵬. "FREE VIBRATION OF ORTHOTROPIC ANNULAR MINDLIN PLATE OF VARIABLE THICKNESS." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/7u3x88.

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碩士 大同大學 機械工程學系(所) 95 Natural frequency of orthotropic annular plates with particular thickness variation is investigated based on Mindlin’s thick plate theory in this study. Also two outer restrained edges: simply -supported and clamped conditions are considered. In other words, the effects of shear deformation and rotary inertia are considered. In order to solve the governing eigenvalue problem, boundary characteristic orthonormal polynomials are applied in Rayleigh-Ritz method. Frequency parameters of the plates are evaluated for different values variables, such as ratio of radii, thickness ratio, thickness constant, taper parameter, orthotropic rigidity ratio, and vibration modes. The numerical convergence of the method is tested and a comparison of results for special cases of isotropic annular plates shows good accuracy. The effects of plate geometry and material properties on frequency parameter are demonstrated in forms of tables and figures. Therefore, in this study, the dynamic characteristics of plates can be predicted accurately by considering all effects of variables for different vibration modes.

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Padhi, Bhabani Sankar. "Free Vibration of Laminated Composite Plate with a Central Hole." Thesis, 2014. http://ethesis.nitrkl.ac.in/6524/1/110CE0048-3.pdf.

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Composite materials find a wide range of application, especially in weight sensitive structures like aircraft, spacecraft due to their high strength-to-weight ratio and high stiffness-to-weight ratio. Laminated plates used in these structures are often subjected to dynamic loads. This necessitates the study of buckling and vibrational characteristics of these plates. The presence of holes in the plates makes the analysis complex. Holes are provided for venting, conveyance, maintenance etc. The presence of holes may alter the nature of vibration of the plates. It is, therefore, important to analyze the vibration of laminated composite plates with holes. Also, the effect of various parameters, e.g. boundary condition, aspect ratio, hole-size, number of layers, fiber orientation etc. needs to be analyzed for a safe and stable design of structures. An orthotropic plate with symmetric fiber orientation was considered for this study. The material properties were fixed. The natural frequencies were computed for different boundary conditions, number of layers, hole-size, aspect ratio, and fiber orientation. The effect of these variables on the nature of vibration is analyzed and discussed. Also, the natural frequencies of a square laminated composite plate with holes of various geometries – circular, square, triangular and hexagonal were computed and compared. ANSYS 13.0 is used for the computation of natural frequencies.

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Sahu, Sibasish. "Free Vibration Study of Sandwich Plate With Different Boundary Conditions." Thesis, 2016. http://ethesis.nitrkl.ac.in/9206/1/2016_MT_SSahu.pdf.

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Vibration is a most important parameter for machine element and engineering structure. Control the vibration of structures is one of the main areas of investigation for the researchers in the modern world. Present work is focused on the analysis of free vibration of the sandwich plate with viscoelastic core under different boundary conditions. To reduce the vibration damper has been used. The viscoelastic material is used as the core of the plate due to its good energy absorbing capacity. The material properties especially silicon rubber polymer for the core are used to show the parametric effect of core thickness ratio, aspect ratio, and length to thickness ratio vs. natural frequency. The experiment has been carried out by considering galvanised steel as face material and silicone rubber polynomial as the core material of the sandwich plate. The specimen is tested under different boundary condition (fixed-fixed, cantilever). Its result is verified in Ansys Workbench 15.0 software package. All the Ansys and experimental result are taken for predicting the natural frequency of the plate in a constant core thickness ratio with the help of AI technique. The analysis concludes the variation of the geometrical parameter with different boundary conditions on the natural frequency. The simulated, AI technique and experiment results show good agreement with each other.

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Lee, Ying-Te, and 李應德. "Free vibration of membrane and plate problems by using meshless methods." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/71066520607835786116.

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碩士 國立臺灣海洋大學 河海工程學系 92 In this thesis, meshless methods by using the imaginary-part, real-part and complex-valued fundamental solutions are utilized to solve free vibration of membrane and plate problems. Single and double-layer potential approaches are both considered for the membrane problem and 6 ( ) options by adopting two potentials from the single, double, triple and quadruple potentials are chosen for the plate problem. Spurious eigenvalues appear in MFS for simply-connected problems by using imaginary-part or real-part fundamental solutions. Even though the complex-valued fundamental solution is employed, the spurious eigenvalues also appear for multiply-connected problems. The occurring mechanism of the spurious eigenvalues for membrane and plate problems in the imaginary-part, real-part and complex-valued formulations were studied analytically. The degenerate kernels and circulants were utilized to derive the true and spurious eigenequations analytically for a circular case in the discrete model. True eigenequation depends on the boundary condition while spurious eigenequation relies on the formulation. Spurious eigenvalues for the multiply-connected eigenproblem are true eigenvalues of the associated simply-connected problem bounded by the fictitious boundary of source distribution. Also, the SVD updating document and Burton & Miller methods are employed to suppress the occurrence of the spurious eigenvalues for the membrane and plate eigenproblems. The SVD updating term is utilized to filter out the spurious eigenequation. Several examples were demonstrated to check the validity of the present formulations.

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孫挺家. "Free vibration analysis of annular of annular plate with variable thickness." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/44484657840467465646.

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碩士 國立中興大學 應用數學系 89 In this paper, analysis of the natural frequencies and mode shapes for free vibration of annular plates with variable thickness are presented. The governing differential equations for free vibration of annular plates with varying mass density and flexural rigidity are derived. They can be reduced to Bessel’s equations or Euler’s equation by selecting suitable expressions, such as power functions, for the distributions of flexural rigidity and mass along the radii of the plates. The general solutions of annular plates with variable thickness are obtained. Therefore, frequencies and mode shapes of free vibration of plates with variable thickness are computed and compared for different values of radii ratio and different boundary conditions. Aside from the frequencies and mode shapes for design purposes, these data can be used as test cases for assessing the accuracy of various approximate methods of solution.

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CHOU, LUN-ZHANG, and 丑倫彰. "Buckling and free vibration analysis of laminated plates by using a partial hybrid plate element." Thesis, 1991. http://ndltd.ncl.edu.tw/handle/03697595424079873556.

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Lin, Sheng-Yih, and 林盛益. "Mathematical analysis and numerical study for free vibration of plate using BEM." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/61159591920267147736.

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碩士 國立海洋大學 河海工程學系 91 Abstract In this thesis, the spurious eigenequations for the simply and multiply-connected plate eigenproblems are studied in the continuous and discrete systems. Since any two boundary integral equations in the plate formulation (4 equations) can be chosen, 6 options can be considered instead of only two approaches (single-layer and double-layer methods, singular and hypersingular equations) are adopted for the eigenproblems of the membrane and acoustic problems. The occurring mechanism of the spurious eigenequation for the simply-connected and multiply-connected plate eigenproblems in the real-part, imaginary-part and complex-valued formulations were studied analytically. For the continuous system, degenerate kernels for the fundamental solution and the Fourier series expansion for the boundary density are employed to derive the true and spurious eigenequations analytically for a circular plate. For the discrete system, the degenerate kernels for the fundamental solution and circulants resulting from the circular boundary are employed to determine the spurious eigenequation. True eigenequation depends on the cases while spurious eigenequation is embedded in each formulation for simply-connected and multiply-connected plates. The spurious eigenvalues for the multiply-connected plate eigenproblem is the true eigenvalue of the associated simply-connected problem with the radius b which is the inner boundary of the multiply-connected domain. Also, we provide three methods (SVD updating technique, Burton & Miller method and CHEEF (CHIEF) method) to suppress the occurrence of the spurious eigenvalues for the free vibration of simply and multiply-connected plate eigenproblems. Several examples were demonstrated to check the validity of the formulation.

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Sahu, Girish Kumar. "Static and free vibration analysis of laminated composite skew plate with and without cutout." Thesis, 2013. http://ethesis.nitrkl.ac.in/5206/1/211ME1178.pdf.

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Most of the structures generally under severe static and dynamic loading and different constrained conditions during their service life. This may lead to bending, buckling and vibration of the structure. Therefore, it is necessary to predict the static and vibration responses of laminated composite plates/skew plates precisely with less computational cost and good accuracy of these complex structures and. A suitable finite element model is proposed and developed based on first order shear deformation theory using ANSYS parametric design language (APDL) code. This is well that, the theory accounts for the linear variation of shear stresses along the longitudinal and thickness direction of the laminates. The model has been discretised using an appropriate four noded isoparametric element (SHELL181) from the ANSYS element library. The free vibration and bending responses are computed using Block-Lanczos and Gauss elimination algorithm steps. The responses like, transverse deflections, normal and shear stresses and natural frequencies of composite laminates are obtained through batch method of APDL code. The convergence test has been done of the developed model for all different cases and compared with those available published literature. Parametric effects (modular ratio, support conditions, ply orientations, number of layers, thickness ratio, geometry of cutout, cutout side to plate side ratio and skew angle) on the static and free vibration responses are discussed in detail.

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Huang-WenHsu and 許黃雯. "Free Vibration Analysis of Composite Sandwich Plates." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/38296736173364332984.

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碩士 國立成功大學 航空太空工程學系碩博士班 100 Analytical solutions to natural frequency analysis has been reported in the classical plate theory. It’s always for the thin plates, but the sandwich plates belong to the thick plates which considers the effect of transverse shear deformation. Besides, the natural frequency of composite sandwich plates will be affected by boundary conditions, material properties and stacking sequence. Therefore, it’s difficult to obtain the exact solutions. For this reason, we follow the model proposed by Moh and Hwu, using Navier Solution to deal with free vibration analysis. However, only the special cases like simply supported symmetric cross-ply composite faces can be solved by Navier Solution. In order to improve it, we introduce Levy Solution and Hamilton Principle with numerical procedure. Then, we get the analytical solution for the general cases of composite sandwich plates.

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Paswan, Ajay Kumar. "Free Vibration and Bending Analysis of Uniformly Distributed Carbon Nanotube Composite Plate Using Finite Element Method." Thesis, 2015. http://ethesis.nitrkl.ac.in/7766/1/2015_Free_Vibration_Paswan.pdf.

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In this work, free vibration and bending behaviour of uniformly distributed carbon nanotube composite plate are analysed. The material properties of single-walled carbon nanotube evaluated through molecular dynamics simulation using LAMMPS software. The effective material properties of the composite plates are obtained using an extended rule of mixture. A finite element model is developed for the single-walled carbon nanotube composite plate using ANSYS Parametric Design Language (APDL) code in ANSYS environment. For the discretization purpose, an eight-noded serendipity shell element is used from the ANSYS library. Subsequently, the validation study is performed through the available published literature. Finally, the parametric study is demonstrated by varying different material and geometrical parameters for free vibration and bending responses of composite plate.

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Hu, Yu-zhi, and 胡育誌. "Free Vibration of Woven Composite Laminate Plates withLateral Holes." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/46635691276551105132.

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碩士 逢甲大學 機械工程學所 99 In this study, the free vibration of woven composite laminate plates with lateral holes is discussed. First, a self-reinforced composite laminate plate is manufactured by hot pressing. Its mechanical properties are measured, the fiber wave is observed, the fiber volume fraction is measured, and then the engineering moduli of the Woven Composite Laminate Plates are calculated using the stiffness averaging method. Second, in order to obtain the natural frequencies and modes, the engineering moduli calculated above are put into ANSYS for the analysis of the plate''s free vibration; the results are then verified. Finally, the effects of different length-to-width ratios, hole sizes, hole locations, and other parameters on the vibration of woven composite laminate plates are determined. The results indicate that when the length-to-width ratios and manufactured hole lengths are established, the frequency decreases as the manufactured hole width increases. Likewise, when the length-to-width ratios and manufactured hole width are established, the frequency decreases as the manufactured hole length increases. The natural frequencies of the fourth mode experienced the greatest amount of variation.

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P, Pratheesh P. "Free Vibration Analysis of Twisted Functionally Graded Material Plates." Thesis, 2014. http://ethesis.nitrkl.ac.in/6522/1/212CE2037-2.pdf.

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The present paper will explore the free vibration behavior of thin twisted functionally graded material (FGM) plates. The vibration analysis is done using finite element method. An 8 noded shell element is used for finite element calculations. To model the FGM section, continuous variation in the material property along the thickness is approximated to a laminated composite section consisting of a number of layers and each layer is considered as isotropic. The material property in each layer is determined using power law. Material density, Young's modulus and Poisson's ratio change along the thickness based on power law. The first order shear deformation theory is used in the analysis of pretwisted FGM plate. Convergence of fundamental frequencies is observed, with an increase in mesh size and the number of layers in the thickness direction. To validate the finite element model, for different boundary conditions, the free vibration results are compared with analytical studies and experimental studies. Having fixed the mesh size and number of layers required to represent the material property variation along the depth, the changes in frequencies with variation in angle of twist and material property index is studied. The effect of geometric variables such as gradient index, aspect ratio, side to thickness ratio and angle of twist on the free vibration of cantilever twisted plates is studied. Temperature dependent material properties are considered as well as nonlinear material property variation along the thickness due to temperature. The influence of thermal gradient along the thickness direction on the free vibration of cantilever twisted plates is studied.

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